OBJECTIVES: This lab is designed to acquaint you with Chi Square goodness of fit test.

DIRECTIONS: Follow the instructions below, answering all questions. Your answers should be in the form of a brief report (Word), to be handed in to the instructor before you leave.
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1.  Data Description:

We are interested in investigating the proportions of four blood types(ABO system). Based on prior data we believe that 34% of people have blood type A, 15% blood type B, 23% blood type AB, and 28% blood type O. We go out to campus and collect a sample of 100 students, and find the following:

A: 12 B: 56 AB: 2 O: 30

  First download the data blood type data or bloodtype excel file

a. What is the null hypothesis in this experiment?

b. What are the expected counts for the four blood types, say A, B, AB, O in this experiment? Do they satisfy the large sample criteria?

c. What test statistic are you using to test the hypothesis? What will the distribution be in a large sample?

d. Plot a group chart for expected frequency and observed frequency. Comment.

Graph-> Chart, select Frequency in Y; and Blood in X; In Data Display :click For each , choose group ; Select Code in Group variables; Put appropriate title, axis label, etc. Click Option, select Cluster: Select Code in Cluster. OK.

e. Carry out the chisquare goodness of fit test. Is the data compatible with your null hypothesis?

Hint: How to do chisquare goodness of fit in Minitab?

name c7 as "deviation", "Calc-> Calculator", store result in c7, expression: (c2-c3)**2/c3;

Then "Calc-> Calculator", store result in c8 ( name it as Chisq), expression: sum(c7).

Compute 1-p-value: "Probability Distribution-> Chi-square", click Cumulative probability; enter appropriate degree of freedom, select c8 (Chisq) in Input column: Enter c9 (name it as '1-pvalue') in Optional storage. OK.

Display your result: "Manip-> Display Data", Select c1-c3, c7-c9 in Display. O.K.

2.   Data Description:

A research wants to conduct an experiment to see whether or not students with children tend to attend school full or part time in a community college. That is, are students with children more likely to attend class part-time?

There are a total of 230 people who participated in our study, but there is one missing case. Thus, our valid number of cases (Valid N) is 229.

Next we see the contingency table.

                   Do you have Children

                    Yes       No

Full Time     31        169

Part Time     15        14
 

a.  Take a glance at the data, what is your guess? Does the parenthood status associate with their school status? Why do you think so?

b.   Perform a chisquare test of independence. What is the Chisq value? Draw your conclusion according to your output.

Hint: Input the contigence table in Minitab, in c1 input 31, 15, in c2 input 169, 14."Stat-> Table-> Chi-square test"; Columns containing the table are:c1-c2. O.K.

3.   Chi-square goodness of fit test applet:

Go to http://www.ruf.rice.edu/~lane/stat_sim/chisq_theor/ . Read the instructions and play with it.